function [J, grad] = cofiCostFunc(params, Y, R, num_users, num_movies, ...
                                  num_features, lambda)
%COFICOSTFUNC Collaborative filtering cost function
%   [J, grad] = COFICOSTFUNC(params, Y, R, num_users, num_movies, ...
%   num_features, lambda) returns the cost and gradient for the
%   collaborative filtering problem.
%

% Unfold the U and W matrices from params
X = reshape(params(1:num_movies*num_features), num_movies, num_features);
Theta = reshape(params(num_movies*num_features+1:end), ...
                num_users, num_features);

            
% You need to return the following values correctly
J = 0;
X_grad = zeros(size(X));
Theta_grad = zeros(size(Theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost function and gradient for collaborative
%               filtering. Concretely, you should first implement the cost
%               function (without regularization) and make sure it is
%               matches our costs. After that, you should implement the 
%               gradient and use the checkCostFunction routine to check
%               that the gradient is correct. Finally, you should implement
%               regularization.
%
% Notes: X - num_movies  x num_features matrix of movie features
%        Theta - num_users  x num_features matrix of user features
%        Y - num_movies x num_users matrix of user ratings of movies
%        R - num_movies x num_users matrix, where R(i, j) = 1 if the 
%            i-th movie was rated by the j-th user
%
% You should set the following variables correctly:
%
%        X_grad - num_movies x num_features matrix, containing the 
%                 partial derivatives w.r.t. to each element of X
%        Theta_grad - num_users x num_features matrix, containing the 
%                     partial derivatives w.r.t. to each element of Theta
%

%将Y无评级部分归零
Y = R .* Y;
%计算预测评分
P = X*Theta';
%将无评价部分归零
P = R .* P;

%J = sum(sum((P.-Y).^2))/2;
J = sum(sum((P.-Y).^2))/2+lambda*sum(sum(X.^2))/2+lambda*sum(sum(Theta.^2))/2;

%%计算偏导
%计算X里的每一行元素对应的偏导
for i = 1:num_movies
  idx = find(R(i, :)==1);
  Thetatemp = Theta(idx,:);
  Ytemp = Y(i,idx);
  X_grad(i,:) = (X(i,:)*Thetatemp'-Ytemp)*Thetatemp + lambda*X(i,:);
end

%计算Theta里的每一行元素对应的偏导
for i = 1:num_users;
  idx = find(R(:, i)==1);
  Xtemp = X(idx,:);
  Ytemp = Y(idx,i);
  Theta_grad(i,:) = (Theta(i,:)*Xtemp'-Ytemp')*Xtemp + lambda*Theta(i,:);
end













% =============================================================

grad = [X_grad(:); Theta_grad(:)];

end
